Calculate the volume and surface area of a cylinder based on the radius and height.
The Cylinder Calculator is a handy tool that allows you to quickly and easily calculate the volume and surface area of a cylinder. The calculator is based on mathematical formulas that utilize the radius and height of the cylinder. This calculator is particularly useful for students, engineers, and anyone working with geometry.
The Cylinder Calculator is suitable for a wide range of users, including:
To use the Cylinder Calculator, simply enter the radius and height of the cylinder. The calculator automatically computes the volume and surface area using the following formulas:
Once you have entered the values, you will receive the results immediately, which you can use for checking calculations or planning projects.
The accuracy of the Cylinder Calculator is based on mathematical formulas that have been tested and proven in practice. Please note that when entering values, they must be in the correct format (for example, meters or centimeters) to obtain accurate results. Small errors in the inputs can affect the final outcome.
When using the Cylinder Calculator, keep the following tips in mind:
Let’s illustrate the calculation with an example. If the radius of the cylinder is 5 cm and the height is 10 cm, the volume is calculated using the formula V = π × r² × h = π × 25 × 10 ≈ 785.4 cubic centimeters. The surface area, on the other hand, is A = 2 × π × r × (r + h) = 2 × π × 5 × 15 ≈ 471.2 square centimeters. These calculations are needed, for example, when estimating how much water a round tank or jar can hold, or how much paint is needed to cover the surface of a column.
The Cylinder Calculator is also used in practical renovation projects, such as calculating the volume of a round well or water tank in liters (1 cubic centimeter = 0.001 liters, so 785.4 cm³ ≈ 0.785 liters). In the construction industry, the calculator is also utilized for estimating the material quantities for columns and pipes. Remember that if you measure the diameter instead of the radius, you must divide the diameter by two before using the calculator – entering the diameter in place of the radius would incorrectly quadruple the calculated volume.
The Cylinder Calculator is also useful in everyday practical situations, such as calculating how many liters of paint are needed to paint the exterior of a round tank or how much water fits into a round rainwater barrel.
A cylinder is one of the most common geometric shapes that we need to measure in everyday life and construction – pipes, tanks, barrels, wells, and pillars are all cylindrical in shape. This calculator calculates the volume and surface area of a cylinder based on the radius (or diameter) and height.
Volume V = π × r² × h
Where r is the radius of the base circle and h is the height of the cylinder. If you know the diameter instead of the radius, remember that the radius is half of the diameter (r = d ÷ 2).
Example: Cylinder with a radius of 0.5 m and height 2 m: V = π × 0.5² × 2 = π × 0.25 × 2 ≈ 1,571 m³ or about 1571 liters.
Total Surface Area A = 2π × r × h + 2π × r²
The formula consists of two parts: the surface area of the mantle (2π × r × h) and the surface area of two base circles (2π × r²). If you only need the surface area of the mantle (for example, to calculate the paintable surface without the ends), use only the first term.
If you know the desired volume and height but not the radius, you can solve for the radius using the formula: r = √(V ÷ (π × h)). This requires calculating the square root – see square root and cube root calculator, which also calculates cube roots quickly.
The calculator gives the result in cubic meters (m³), but in everyday life, volume is often expressed in liters. One cubic meter is 1000 liters, so multiply the result by a thousand to get the amount in liters. If the measurements are in centimeters, convert them to meters first (divide by one hundred) before calculating, or use the calculator's centimeter option directly.
The garden rainwater barrel has a diameter of 60 cm (radius 0.3 m) and a height of 90 cm (0.9 m). Volume: π × 0.3² × 0.9 = π × 0.09 × 0.9 ≈ 0,254 m³ or about 254 liters – a typical household rainwater barrel size.
The volume of a cylinder is calculated using the formula V = π × r² × h, where r is the radius of the base circle and h is the height.
Calculate the volume first in cubic meters using the formula V = π × r² × h and multiply the result by a thousand, since one cubic meter is 1000 liters.
The diameter is the width of the circle from edge to edge, the radius is half of that. If you only know the diameter, divide it by two before placing it in the formula.
Total surface area is A = 2π × r × h + 2π × r². If you only need the lateral surface area without the ends, use just the term 2π × r × h.
Solve from the formula r = √(V ÷ (π × h)). This requires calculating the square root – use our square root calculator for a quick result.